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A048102 Numbers k such that if k = Product p_i^e_i then p_i = e_i for all i.

%I A048102 #51 Jan 22 2024 06:11:00
%S A048102 1,4,27,108,3125,12500,84375,337500,823543,3294172,22235661,88942644,
%T A048102 2573571875,10294287500,69486440625,277945762500,285311670611,
%U A048102 1141246682444,7703415106497,30813660425988,302875106592253,891598970659375,1211500426369012,3566395882637500
%N A048102 Numbers k such that if k = Product p_i^e_i then p_i = e_i for all i.
%H A048102 Alois P. Heinz, <a href="/A048102/b048102.txt">Table of n, a(n) for n = 1..10000</a> (first 1038 terms from T. D. Noe)
%H A048102 Daniel Mondot, <a href="/A048102/a048102_2.txt">Table of n, a(n) for n = 1..10000 with factorizations</a>
%F A048102 A027748(a(n),k) = A124010(a(n),k) for k = 1 .. A001221(a(n)). - _Reinhard Zumkeller_, Jan 21 2012
%F A048102 Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/p^p) = 1.2967126856... - _Amiram Eldar_, Oct 13 2020
%e A048102 3^3*5^5 = 84375.
%o A048102 (Haskell)
%o A048102 import Data.Set (empty, fromList, deleteFindMin, union)
%o A048102 import qualified Data.Set as Set (null, map)
%o A048102 a048102 n = a048102_list !! (n-1)
%o A048102 a048102_list = 1 : f empty [1] a051674_list where
%o A048102   f s ys pps'@(pp:pps)
%o A048102     | Set.null s = f (fromList (map (* pp) ys)) (pp:ys) pps
%o A048102     | pp < m     = f (s `union` Set.map (* pp) s `union`
%o A048102                       fromList (map (* pp) ys)) ys pps
%o A048102     | otherwise  = m : f s' (m:ys) pps'
%o A048102     where (m,s') = deleteFindMin s
%o A048102 -- _Reinhard Zumkeller_, Jan 21 2012
%o A048102 (PARI) isok(n) = my(f = factor(n)); for (k=1, #f~, if (f[k,1] != f[k,2], return(0))); 1; \\ _Michel Marcus_, Apr 29 2016
%Y A048102 Cf. A027748, A048103, A048104, A051674, A072873, A124010.
%K A048102 nonn,easy,nice
%O A048102 1,2
%A A048102 _N. J. A. Sloane_
%E A048102 More terms from _Naohiro Nomoto_, Jun 28 2001